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Ilya [14]
2 years ago
9

Problem 4 the measure of the largest angle of a triangle is 90◦ more than the measure of the smallest angle, and the measure of

the remaining angle is 30◦ more than the measure of the smallest angle. find the measure of each angle. showyourwork in obtaining your answe
Mathematics
1 answer:
azamat2 years ago
7 0
Answer:  The measurements of the angles are:  110° ;  50° ;  20°  .<span>
_________________________________________________________
Explanation:
________________________________________________________
Note:  There are 3 (three) angles in any triangle (by definition).

By definition, all the angles in any triangle add up to 180</span>° .<span>
________________________________________________________
The problems asks us to find the measure of EACH angle of the triangle.

We can set up an equation; given the information in the problem; to solve for the measure of EACH of the 3 (THREE) angles in the triangle:
________________________________________________________
     </span>→  " <span>x + (x + 90) + (x + 30) = 180 "  ;
_____________________________________________
   in which:  "x" is the measure of one of the angles;
                                (specifically, the smallest angle) in the triangle;
              "(x + 90)" is the measure of another one of the angles in the triangle; 
              </span>"(x + 30)" is the measure of another one of the angles in the triangle; <span>
___________________________________________________________
By solving for "x" in the equation; we can solve for the measures of all the angles in the triangle;
_________________________________________________
</span>  →   x + (x + 90) + (x + 30) = 180 ; 
<span>
         x + x + 90 + x + 30 = 180 ;
        
  </span>→<span>    3x + 120 = 180 ;
______________________________________
     Subtract "120" from each side of the equation ;

           3x + 120 </span>− 120 = 180 <span>− 120 ;
</span><span>
to get:      3x  = 60 ;
________________________________
   Now, divide EACH SIDE of the equation by "3" ; to isolate "x" on one side of the <span>equation ;  and</span> to solve for "x" ;

               3x = 60 ;
            
              3x / 3 = 60 / 3 ;
             
                 x = 20 ;
_________________________________________
Now, we have the original equation:
__________________________________
</span>x + (x + 90) + (x + 30) = 180 ; 
<span>
in which:  x = 20</span>° {the smallest angle) ; 
                "(x + 90)" = "(20 + 90) = 110° ;
                "(x + 30)" = "(20 + 30)" = 50° ;
<span>__________________________________________________________
Answer:  The measurements of the angles are:  110</span>° ;  50° ;  20°  .
<span>__________________________________________________________
To check our work:

20 + 110 + 50 =?  180 ?? ;   </span>→ 130 + 50 =?  180 ?? ; → Yes!
<span>_____________________________________________________

</span>
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